Even-hole-free graphIn the mathematical area of graph theory, a graph is even-hole-free if it contains no induced cycle with an even number of vertices. More precisely, the definition may allow the graph to have induced cycles of length four, or may also disallow them: the latter is referred to as even-cycle-free graphs. demonstrated that every even-hole-free graph contains a bisimplicial vertex, which settled a conjecture by Reed. gave the first polynomial time recognition algorithm for even-hole-free graphs, which runs in time.
Hungarian algorithmThe Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal–dual methods. It was developed and published in 1955 by Harold Kuhn, who gave the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians: Dénes Kőnig and Jenő Egerváry. James Munkres reviewed the algorithm in 1957 and observed that it is (strongly) polynomial.
Existential theory of the realsIn mathematical logic, computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the form where the variables are interpreted as having real number values, and where is a quantifier-free formula involving equalities and inequalities of real polynomials. A sentence of this form is true if it is possible to find values for all of the variables that, when substituted into formula , make it become true.
Cyclic permutationIn mathematics, and in particular in group theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation has k elements, it may be called a k-cycle. Some authors widen this definition to include permutations with fixed points in addition to at most one non-trivial cycle. In cycle notation, cyclic permutations are denoted by the list of their elements enclosed with parentheses, in the order to which they are permuted.
